TSTP Solution File: SET668+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET668+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 03:36:28 EDT 2022
% Result : Theorem 49.35s 49.59s
% Output : CNFRefutation 49.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 176 ( 39 unt; 0 def)
% Number of atoms : 627 ( 57 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 798 ( 347 ~; 320 |; 71 &)
% ( 15 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 298 ( 7 sgn 154 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,C))
=> ( subset(identity_relation_of(D),E)
=> ( subset(D,domain(B,C,E))
& subset(D,range(B,C,E)) ) ) ) ) ) ) ).
fof(p7,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ) ).
fof(p9,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( B = C
<=> ( subset(B,C)
& subset(C,B) ) ) ) ) ).
fof(p16,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ) ).
fof(p20,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ) ).
fof(p21,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ) ).
fof(p22,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ) ).
fof(p28,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> domain(B,C,D) = domain_of(D) ) ) ) ).
fof(p29,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(domain(B,C,D),subset_type(B)) ) ) ) ).
fof(p30,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> range(B,C,D) = range_of(D) ) ) ) ).
fof(p32,axiom,
! [B] : ilf_type(B,set_type) ).
fof(prove_relset_1_31,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( subset(identity_relation_of(C),D)
=> ( C = domain(C,B,D)
& subset(C,range(C,B,D)) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ( ilf_type(D,relation_type(C,B))
& subset(identity_relation_of(C),D) )
=> C = domain(C,B,D) ) ) ),
inference(strip,[],[prove_relset_1_31]) ).
fof(subgoal_1,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ( ilf_type(D,relation_type(C,B))
& subset(identity_relation_of(C),D)
& C = domain(C,B,D) )
=> subset(C,range(C,B,D)) ) ) ),
inference(strip,[],[prove_relset_1_31]) ).
fof(negate_0_0,plain,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ( ilf_type(D,relation_type(C,B))
& subset(identity_relation_of(C),D) )
=> C = domain(C,B,D) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( C != domain(C,B,D)
& ilf_type(D,relation_type(C,B))
& subset(identity_relation_of(C),D) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p32]) ).
fof(normalize_0_2,plain,
! [B] : ilf_type(B,set_type),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
? [B,C] :
( ilf_type(C,set_type)
& ? [D] :
( C != domain(C,B,D)
& ilf_type(D,relation_type(C,B))
& subset(identity_relation_of(C),D) ) ),
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
fof(normalize_0_4,plain,
( ilf_type(skolemFOFtoCNF_C_4,set_type)
& ? [D] :
( skolemFOFtoCNF_C_4 != domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,D)
& ilf_type(D,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
& subset(identity_relation_of(skolemFOFtoCNF_C_4),D) ) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
? [D] :
( skolemFOFtoCNF_C_4 != domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,D)
& ilf_type(D,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
& subset(identity_relation_of(skolemFOFtoCNF_C_4),D) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
( skolemFOFtoCNF_C_4 != domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5)
& ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
& subset(identity_relation_of(skolemFOFtoCNF_C_4),skolemFOFtoCNF_D_5) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
subset(identity_relation_of(skolemFOFtoCNF_C_4),skolemFOFtoCNF_D_5),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_9,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| ( subset(D,domain(B,C,E))
& subset(D,range(B,C,E)) ) ) ) ) ),
inference(canonicalize,[],[p2]) ).
fof(normalize_0_10,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| ( subset(D,domain(B,C,E))
& subset(D,range(B,C,E)) ) ) ) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B,C,D,E] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,domain(B,C,E)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,range(B,C,E)) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B,C,D,E] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,domain(B,C,E)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ) ) ),
inference(canonicalize,[],[p28]) ).
fof(normalize_0_14,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ) ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ) ) ),
inference(canonicalize,[],[p9]) ).
fof(normalize_0_17,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ) ) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [B,C] :
( ( B != C
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| subset(B,C) )
& ( B != C
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| subset(C,B) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ subset(B,C)
| ~ subset(C,B)
| B = C ) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& ilf_type(D,set_type)
& member(D,B) ) ) ) ),
inference(canonicalize,[],[p7]) ).
fof(normalize_0_21,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& ilf_type(D,set_type)
& member(D,B) ) ) ) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| subset(B,C) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ilf_type(skolemFOFtoCNF_D_1(B,C),set_type)
| subset(B,C) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ) ),
inference(clausify,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) ),
inference(conjunct,[],[normalize_0_22]) ).
fof(normalize_0_25,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| empty(C)
| ( ~ ilf_type(B,member_type(C))
<=> ~ member(B,C) ) ) ),
inference(canonicalize,[],[p22]) ).
fof(normalize_0_26,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| empty(C)
| ( ~ ilf_type(B,member_type(C))
<=> ~ member(B,C) ) ) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [B,C] :
( ( ~ ilf_type(B,member_type(C))
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [B,C] :
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ ilf_type(C,member_type(power_set(B)))
<=> ~ ilf_type(C,subset_type(B)) ) ) ),
inference(canonicalize,[],[p16]) ).
fof(normalize_0_30,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ ilf_type(C,member_type(power_set(B)))
<=> ~ ilf_type(C,subset_type(B)) ) ) ),
inference(specialize,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
! [B,C] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,set_type)
| ilf_type(C,subset_type(B)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ) ),
inference(clausify,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(conjunct,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ) ) ),
inference(canonicalize,[],[p29]) ).
fof(normalize_0_34,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ) ) ),
inference(specialize,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ),
inference(clausify,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(canonicalize,[],[p21]) ).
fof(normalize_0_37,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(specialize,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
! [B] :
( ( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) )
& ( ~ ilf_type(B,set_type)
| ilf_type(power_set(B),set_type) ) ),
inference(clausify,[],[normalize_0_37]) ).
fof(normalize_0_39,plain,
! [B] :
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ member(B,power_set(C))
<=> ? [D] :
( ~ member(D,C)
& ilf_type(D,set_type)
& member(D,B) ) ) ) ),
inference(canonicalize,[],[p20]) ).
fof(normalize_0_41,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ member(B,power_set(C))
<=> ? [D] :
( ~ member(D,C)
& ilf_type(D,set_type)
& member(D,B) ) ) ) ),
inference(specialize,[],[normalize_0_40]) ).
fof(normalize_0_42,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_3(B,C),C)
| member(B,power_set(C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ilf_type(skolemFOFtoCNF_D_3(B,C),set_type)
| member(B,power_set(C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(B,power_set(C))
| member(skolemFOFtoCNF_D_3(B,C),B) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ) ),
inference(clausify,[],[normalize_0_41]) ).
fof(normalize_0_43,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(conjunct,[],[normalize_0_42]) ).
fof(normalize_0_44,plain,
skolemFOFtoCNF_C_4 != domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
subset(identity_relation_of(skolemFOFtoCNF_C_4),skolemFOFtoCNF_D_5),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_1,plain,
ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_2,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,domain(B,C,E)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_3,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_4,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,domain(B,C,E)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_0_3:[bind(B,$fot(C))]]) ).
cnf(refute_0_6,plain,
( ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,domain(B,C,E)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
ilf_type(D,set_type),
inference(subst,[],[refute_0_3:[bind(B,$fot(D))]]) ).
cnf(refute_0_8,plain,
( ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,domain(B,C,E)) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
| ~ subset(identity_relation_of(X_3204),skolemFOFtoCNF_D_5)
| subset(X_3204,domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5)) ),
inference(subst,[],[refute_0_8:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(X_3204)),bind(E,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_10,plain,
( ~ subset(identity_relation_of(X_3204),skolemFOFtoCNF_D_5)
| subset(X_3204,domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5)) ),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_12,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_5,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
| domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5) = domain_of(skolemFOFtoCNF_D_5) ),
inference(subst,[],[refute_0_13:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_15,plain,
domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5) = domain_of(skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) )],[refute_0_1,refute_0_14]) ).
cnf(refute_0_16,plain,
( domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5) != domain_of(skolemFOFtoCNF_D_5)
| ~ subset(X_3204,domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5))
| subset(X_3204,domain_of(skolemFOFtoCNF_D_5)) ),
introduced(tautology,[equality,[$cnf( subset(X_3204,domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5)) ),[1],$fot(domain_of(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_17,plain,
( ~ subset(X_3204,domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5))
| subset(X_3204,domain_of(skolemFOFtoCNF_D_5)) ),
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),domain_of(skolemFOFtoCNF_D_5)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ subset(identity_relation_of(X_3204),skolemFOFtoCNF_D_5)
| subset(X_3204,domain_of(skolemFOFtoCNF_D_5)) ),
inference(resolve,[$cnf( subset(X_3204,domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5)) )],[refute_0_10,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ subset(identity_relation_of(skolemFOFtoCNF_C_4),skolemFOFtoCNF_D_5)
| subset(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_5)) ),
inference(subst,[],[refute_0_18:[bind(X_3204,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_20,plain,
subset(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_5)),
inference(resolve,[$cnf( subset(identity_relation_of(skolemFOFtoCNF_C_4),skolemFOFtoCNF_D_5) )],[refute_0_0,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_22,plain,
( ~ ilf_type(C,set_type)
| ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_5,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ subset(domain_of(skolemFOFtoCNF_D_5),skolemFOFtoCNF_C_4)
| ~ subset(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_5))
| skolemFOFtoCNF_C_4 = domain_of(skolemFOFtoCNF_D_5) ),
inference(subst,[],[refute_0_23:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(domain_of(skolemFOFtoCNF_D_5)))]]) ).
cnf(refute_0_25,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_26,plain,
( ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| subset(B,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ member(skolemFOFtoCNF_D_1(B,C),C)
| subset(B,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_5,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ member(skolemFOFtoCNF_D_1(domain_of(skolemFOFtoCNF_D_5),skolemFOFtoCNF_C_4),skolemFOFtoCNF_C_4)
| subset(domain_of(skolemFOFtoCNF_D_5),skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_27:[bind(B,$fot(domain_of(skolemFOFtoCNF_D_5))),bind(C,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_29,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_30,plain,
( ~ ilf_type(C,set_type)
| member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_29]) ).
cnf(refute_0_31,plain,
( member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_5,refute_0_30]) ).
cnf(refute_0_32,plain,
( member(skolemFOFtoCNF_D_1(domain_of(skolemFOFtoCNF_D_5),C),domain_of(skolemFOFtoCNF_D_5))
| subset(domain_of(skolemFOFtoCNF_D_5),C) ),
inference(subst,[],[refute_0_31:[bind(B,$fot(domain_of(skolemFOFtoCNF_D_5)))]]) ).
cnf(refute_0_33,plain,
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_34,plain,
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ ilf_type(B,member_type(C))
| empty(C)
| member(B,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_5,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),member_type(power_set(skolemFOFtoCNF_C_4)))
| empty(power_set(skolemFOFtoCNF_C_4))
| member(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),power_set(skolemFOFtoCNF_C_4)) ),
inference(subst,[],[refute_0_35:[bind(B,$fot(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5))),bind(C,$fot(power_set(skolemFOFtoCNF_C_4)))]]) ).
cnf(refute_0_37,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_38,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_5,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),subset_type(skolemFOFtoCNF_C_4))
| ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),member_type(power_set(skolemFOFtoCNF_C_4))) ),
inference(subst,[],[refute_0_39:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5)))]]) ).
cnf(refute_0_41,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_42,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_5,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
| ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),subset_type(skolemFOFtoCNF_C_4)) ),
inference(subst,[],[refute_0_43:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_45,plain,
ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),subset_type(skolemFOFtoCNF_C_4)),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) )],[refute_0_1,refute_0_44]) ).
cnf(refute_0_46,plain,
ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),member_type(power_set(skolemFOFtoCNF_C_4))),
inference(resolve,[$cnf( ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),subset_type(skolemFOFtoCNF_C_4)) )],[refute_0_45,refute_0_40]) ).
cnf(refute_0_47,plain,
( empty(power_set(skolemFOFtoCNF_C_4))
| member(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),power_set(skolemFOFtoCNF_C_4)) ),
inference(resolve,[$cnf( ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),member_type(power_set(skolemFOFtoCNF_C_4))) )],[refute_0_46,refute_0_36]) ).
cnf(refute_0_48,plain,
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_49,plain,
~ empty(power_set(B)),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_48]) ).
cnf(refute_0_50,plain,
~ empty(power_set(skolemFOFtoCNF_C_4)),
inference(subst,[],[refute_0_49:[bind(B,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_51,plain,
member(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),power_set(skolemFOFtoCNF_C_4)),
inference(resolve,[$cnf( empty(power_set(skolemFOFtoCNF_C_4)) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
( domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5) != domain_of(skolemFOFtoCNF_D_5)
| ~ member(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),power_set(skolemFOFtoCNF_C_4))
| member(domain_of(skolemFOFtoCNF_D_5),power_set(skolemFOFtoCNF_C_4)) ),
introduced(tautology,[equality,[$cnf( member(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),power_set(skolemFOFtoCNF_C_4)) ),[0],$fot(domain_of(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_53,plain,
( ~ member(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),power_set(skolemFOFtoCNF_C_4))
| member(domain_of(skolemFOFtoCNF_D_5),power_set(skolemFOFtoCNF_C_4)) ),
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),domain_of(skolemFOFtoCNF_D_5)) )],[refute_0_15,refute_0_52]) ).
cnf(refute_0_54,plain,
member(domain_of(skolemFOFtoCNF_D_5),power_set(skolemFOFtoCNF_C_4)),
inference(resolve,[$cnf( member(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),power_set(skolemFOFtoCNF_C_4)) )],[refute_0_51,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_43]) ).
cnf(refute_0_56,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_5,refute_0_56]) ).
cnf(refute_0_58,plain,
( ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_0_7,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ member(X_686,domain_of(skolemFOFtoCNF_D_5))
| ~ member(domain_of(skolemFOFtoCNF_D_5),power_set(skolemFOFtoCNF_C_4))
| member(X_686,skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_58:[bind(B,$fot(domain_of(skolemFOFtoCNF_D_5))),bind(C,$fot(skolemFOFtoCNF_C_4)),bind(D,$fot(X_686))]]) ).
cnf(refute_0_60,plain,
( ~ member(X_686,domain_of(skolemFOFtoCNF_D_5))
| member(X_686,skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( member(domain_of(skolemFOFtoCNF_D_5),power_set(skolemFOFtoCNF_C_4)) )],[refute_0_54,refute_0_59]) ).
cnf(refute_0_61,plain,
( ~ member(skolemFOFtoCNF_D_1(domain_of(skolemFOFtoCNF_D_5),C),domain_of(skolemFOFtoCNF_D_5))
| member(skolemFOFtoCNF_D_1(domain_of(skolemFOFtoCNF_D_5),C),skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_60:[bind(X_686,$fot(skolemFOFtoCNF_D_1(domain_of(skolemFOFtoCNF_D_5),C)))]]) ).
cnf(refute_0_62,plain,
( member(skolemFOFtoCNF_D_1(domain_of(skolemFOFtoCNF_D_5),C),skolemFOFtoCNF_C_4)
| subset(domain_of(skolemFOFtoCNF_D_5),C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(domain_of(skolemFOFtoCNF_D_5),C),domain_of(skolemFOFtoCNF_D_5)) )],[refute_0_32,refute_0_61]) ).
cnf(refute_0_63,plain,
( member(skolemFOFtoCNF_D_1(domain_of(skolemFOFtoCNF_D_5),skolemFOFtoCNF_C_4),skolemFOFtoCNF_C_4)
| subset(domain_of(skolemFOFtoCNF_D_5),skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_62:[bind(C,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_64,plain,
subset(domain_of(skolemFOFtoCNF_D_5),skolemFOFtoCNF_C_4),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(domain_of(skolemFOFtoCNF_D_5),skolemFOFtoCNF_C_4),skolemFOFtoCNF_C_4) )],[refute_0_63,refute_0_28]) ).
cnf(refute_0_65,plain,
( ~ subset(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_5))
| skolemFOFtoCNF_C_4 = domain_of(skolemFOFtoCNF_D_5) ),
inference(resolve,[$cnf( subset(domain_of(skolemFOFtoCNF_D_5),skolemFOFtoCNF_C_4) )],[refute_0_64,refute_0_24]) ).
cnf(refute_0_66,plain,
skolemFOFtoCNF_C_4 != domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_67,plain,
( domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5) != domain_of(skolemFOFtoCNF_D_5)
| skolemFOFtoCNF_C_4 != domain_of(skolemFOFtoCNF_D_5)
| skolemFOFtoCNF_C_4 = domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_C_4,domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5)) ),[1],$fot(domain_of(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_68,plain,
( skolemFOFtoCNF_C_4 != domain_of(skolemFOFtoCNF_D_5)
| skolemFOFtoCNF_C_4 = domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5) ),
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),domain_of(skolemFOFtoCNF_D_5)) )],[refute_0_15,refute_0_67]) ).
cnf(refute_0_69,plain,
skolemFOFtoCNF_C_4 != domain_of(skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_4,domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5)) )],[refute_0_68,refute_0_66]) ).
cnf(refute_0_70,plain,
~ subset(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_5)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_5)) )],[refute_0_65,refute_0_69]) ).
cnf(refute_0_71,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_5)) )],[refute_0_20,refute_0_70]) ).
fof(negate_1_0,plain,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ( ilf_type(D,relation_type(C,B))
& subset(identity_relation_of(C),D)
& C = domain(C,B,D) )
=> subset(C,range(C,B,D)) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( ~ subset(C,range(C,B,D))
& C = domain(C,B,D)
& ilf_type(D,relation_type(C,B))
& subset(identity_relation_of(C),D) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p32]) ).
fof(normalize_1_2,plain,
! [B] : ilf_type(B,set_type),
inference(specialize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
? [B,C] :
( ilf_type(C,set_type)
& ? [D] :
( ~ subset(C,range(C,B,D))
& C = domain(C,B,D)
& ilf_type(D,relation_type(C,B))
& subset(identity_relation_of(C),D) ) ),
inference(simplify,[],[normalize_1_0,normalize_1_2]) ).
fof(normalize_1_4,plain,
( ilf_type(skolemFOFtoCNF_C_5,set_type)
& ? [D] :
( ~ subset(skolemFOFtoCNF_C_5,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D))
& skolemFOFtoCNF_C_5 = domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D)
& ilf_type(D,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
& subset(identity_relation_of(skolemFOFtoCNF_C_5),D) ) ),
inference(skolemize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
? [D] :
( ~ subset(skolemFOFtoCNF_C_5,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D))
& skolemFOFtoCNF_C_5 = domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D)
& ilf_type(D,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
& subset(identity_relation_of(skolemFOFtoCNF_C_5),D) ),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
( ~ subset(skolemFOFtoCNF_C_5,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6))
& skolemFOFtoCNF_C_5 = domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6)
& ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
& subset(identity_relation_of(skolemFOFtoCNF_C_5),skolemFOFtoCNF_D_6) ),
inference(skolemize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
subset(identity_relation_of(skolemFOFtoCNF_C_5),skolemFOFtoCNF_D_6),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_9,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| ( subset(D,domain(B,C,E))
& subset(D,range(B,C,E)) ) ) ) ) ),
inference(canonicalize,[],[p2]) ).
fof(normalize_1_10,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| ( subset(D,domain(B,C,E))
& subset(D,range(B,C,E)) ) ) ) ) ),
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [B,C,D,E] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,domain(B,C,E)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,range(B,C,E)) ) ),
inference(clausify,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [B,C,D,E] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,range(B,C,E)) ),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ) ) ),
inference(canonicalize,[],[p30]) ).
fof(normalize_1_14,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ) ) ),
inference(specialize,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(clausify,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
~ subset(skolemFOFtoCNF_C_5,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6)),
inference(conjunct,[],[normalize_1_6]) ).
cnf(refute_1_0,plain,
subset(identity_relation_of(skolemFOFtoCNF_C_5),skolemFOFtoCNF_D_6),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_1,plain,
ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_2,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,range(B,C,E)) ),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_3,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_4,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,range(B,C,E)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_2]) ).
cnf(refute_1_5,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_1_3:[bind(B,$fot(C))]]) ).
cnf(refute_1_6,plain,
( ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,range(B,C,E)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_4]) ).
cnf(refute_1_7,plain,
ilf_type(D,set_type),
inference(subst,[],[refute_1_3:[bind(B,$fot(D))]]) ).
cnf(refute_1_8,plain,
( ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,range(B,C,E)) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_1_7,refute_1_6]) ).
cnf(refute_1_9,plain,
( ~ ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
| ~ subset(identity_relation_of(X_7894),skolemFOFtoCNF_D_6)
| subset(X_7894,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6)) ),
inference(subst,[],[refute_1_8:[bind(B,$fot(skolemFOFtoCNF_C_5)),bind(C,$fot(skolemFOFtoCNF_B_2)),bind(D,$fot(X_7894)),bind(E,$fot(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_1_10,plain,
( ~ subset(identity_relation_of(X_7894),skolemFOFtoCNF_D_6)
| subset(X_7894,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6)) ),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)) )],[refute_1_1,refute_1_9]) ).
cnf(refute_1_11,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_12,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_11]) ).
cnf(refute_1_13,plain,
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_12]) ).
cnf(refute_1_14,plain,
( ~ ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
| range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6) = range_of(skolemFOFtoCNF_D_6) ),
inference(subst,[],[refute_1_13:[bind(B,$fot(skolemFOFtoCNF_C_5)),bind(C,$fot(skolemFOFtoCNF_B_2)),bind(D,$fot(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_1_15,plain,
range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6) = range_of(skolemFOFtoCNF_D_6),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)) )],[refute_1_1,refute_1_14]) ).
cnf(refute_1_16,plain,
( range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6) != range_of(skolemFOFtoCNF_D_6)
| ~ subset(X_7894,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6))
| subset(X_7894,range_of(skolemFOFtoCNF_D_6)) ),
introduced(tautology,[equality,[$cnf( subset(X_7894,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6)) ),[1],$fot(range_of(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_1_17,plain,
( ~ subset(X_7894,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6))
| subset(X_7894,range_of(skolemFOFtoCNF_D_6)) ),
inference(resolve,[$cnf( $equal(range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6),range_of(skolemFOFtoCNF_D_6)) )],[refute_1_15,refute_1_16]) ).
cnf(refute_1_18,plain,
( ~ subset(identity_relation_of(X_7894),skolemFOFtoCNF_D_6)
| subset(X_7894,range_of(skolemFOFtoCNF_D_6)) ),
inference(resolve,[$cnf( subset(X_7894,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6)) )],[refute_1_10,refute_1_17]) ).
cnf(refute_1_19,plain,
( ~ subset(identity_relation_of(skolemFOFtoCNF_C_5),skolemFOFtoCNF_D_6)
| subset(skolemFOFtoCNF_C_5,range_of(skolemFOFtoCNF_D_6)) ),
inference(subst,[],[refute_1_18:[bind(X_7894,$fot(skolemFOFtoCNF_C_5))]]) ).
cnf(refute_1_20,plain,
subset(skolemFOFtoCNF_C_5,range_of(skolemFOFtoCNF_D_6)),
inference(resolve,[$cnf( subset(identity_relation_of(skolemFOFtoCNF_C_5),skolemFOFtoCNF_D_6) )],[refute_1_0,refute_1_19]) ).
cnf(refute_1_21,plain,
~ subset(skolemFOFtoCNF_C_5,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6)),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_22,plain,
( range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6) != range_of(skolemFOFtoCNF_D_6)
| ~ subset(skolemFOFtoCNF_C_5,range_of(skolemFOFtoCNF_D_6))
| subset(skolemFOFtoCNF_C_5,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6)) ),
introduced(tautology,[equality,[$cnf( ~ subset(skolemFOFtoCNF_C_5,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6)) ),[1],$fot(range_of(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_1_23,plain,
( ~ subset(skolemFOFtoCNF_C_5,range_of(skolemFOFtoCNF_D_6))
| subset(skolemFOFtoCNF_C_5,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6)) ),
inference(resolve,[$cnf( $equal(range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6),range_of(skolemFOFtoCNF_D_6)) )],[refute_1_15,refute_1_22]) ).
cnf(refute_1_24,plain,
~ subset(skolemFOFtoCNF_C_5,range_of(skolemFOFtoCNF_D_6)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_5,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6)) )],[refute_1_23,refute_1_21]) ).
cnf(refute_1_25,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_5,range_of(skolemFOFtoCNF_D_6)) )],[refute_1_20,refute_1_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.11 % Problem : SET668+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 10:48:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 49.35/49.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 49.35/49.59
% 49.35/49.59 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 49.35/49.61
%------------------------------------------------------------------------------